I had to ask Natalia

Natalia Kills is wearing a vintage fifties coat bought at a flea market in LA. No not the monthly Rose Bowl, somewhere smaller that opens weekly. She mentioned that in London around Spitalsfield market there's a vintage shop called Retro Woman that has the exact same coats. Also Etsy if you type in 'fifties fur collar swing coat.'
Her sunglasses are by Karen Walker.

I stopped her walking out of Tea and Sympathy in the west village (yes I left my lunch to run out and tap her on the shoulder).